Planar Mesh Research Articles

Isoradial meshes: Covering elastic gridshells with planar facets

Abstract Elastic gridshells are structures made of flat two-way grids which are deformed elastically before they are braced and which afterwards mechanically behave like continuous shells. Gridshells present some advantages in terms of manufacturing, lightness and time of assembly. Their covering remains however a technical issue. The present article proposes hence an alternative method to cover them by planar quadrilateral facets, which could also be used as natural bracing if connected properly. It relies on the duality between a certain family of circular meshes with a unique radius and some Tchebycheff nets. The approach is versatile and allows for the design of a large variety of shapes from two curves in space. Real time numerical tools are developed for open and closed curves as well as a strategy for umbilical points. The relaxation of the Tchebycheff net shows finally that an equilibrium configuration can be found in the vicinity of the planar quadrilateral mesh (PQ-Mesh) which confirm the practical feasibility of elastic gridshells covered with planar facets.

A Constrained Resampling Strategy for Mesh Improvement

AbstractIn many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously. We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state‐of‐the‐art.

Towards a new definition of areal surface texture parameters on freeform surface

Current definitions and computation of areal surface texture parameters are based on planar, measured or unwrapped, surface which is not applicable for non planar irregular meshes. In this paper an extension of areal surface texture parameters (height and hybrid parameters) for freeform surface is proposed. The proposed method can be used for both general and complex surfaces and it works well on surfaces where there are undercuts and non uniformly spaced points. The proposed method has been tested on six sets of different types of surfaces and the computed parameter results were compared with the values of the parameters defined in ISO 25178-2:2012.

Enhancing Urban Façades via LiDAR‐Based Sculpting

AbstractBuildings with symmetrical façades are ubiquitous in urban landscapes and detailed models of these buildings enhance the visual realism of digital urban scenes. However, a vast majority of the existing urban building models in web‐based 3D maps such as Google earth are either less detailed or heavily rely on texturing to render the details. We present a new framework for enhancing the details of such coarse models, using the geometry and symmetry inferred from the light detection and ranging (LiDAR) scans and 2D templates. The user‐defined 2D templates, referred to as coded planar meshes (CPMs), encodes the geometry of the smallest repeating 3D structures of the façades via face codes. Our encoding scheme, take into account the directions, type as well as the offset distance of the sculpting to be applied at the respective locations on the coarse model. In our approach, LiDAR scan is registered with the coarse models taken from Google earth 3D or Bing maps 3D and decomposed into dominant planar segments (each representing the frontal or lateral walls of the building). The façade segments are then split into horizontal and vertical tiles using a weighted point count function defined over the window or door boundaries. This is followed by an automatic identification of CPM locations with the help of a template fitting algorithm that respects the alignment regularity as well as the inter‐element spacing on the façade layout. Finally, 3D boolean sculpting operations are applied over the boxes induced by CPMs and the coarse model, and a detailed 3D model is generated. The proposed framework is capable of modelling details even with occluded scans and enhances not only the frontal façades (facing to the streets) but also the lateral façades of the buildings. We demonstrate the potentials of the proposed framework by providing several examples of enhanced Google earth models and highlight the advantages of our method when designing photo‐realistic urban façades.

Three-dimensional modelling of heat conduction in laminated plates with the use of a two-dimensional numerical model

This paper presents a two-dimensional numerical (2D) model for analysing the full three-dimensional (3D) problem of heat transport problems in laminated composite plates. A 2D finite element model is enough for good representation of a 3D problem since each single node in the mesh has enough degrees of freedom associated with particular layers of the laminated plate. The 2D numerical model is quite simple and effective and it allows considering multi-layered structures in which individual layers are made of different materials and the structure may consist of a combination of thick and very thin layers without numerical instabilities. The method presented in this paper is combined with a specially tailored postprocessing procedure so that results from the planar mesh can be visualised as 3D graphics. The paper is illustrated with a set of examples in which stationary and non-stationary problems are considered. In these examples modelling of the laminated glass with three glass panes and thin layers of bonding material is presented.

Guaranteed quality isotropic surface remeshing based on uniformization

Surface remeshing plays a significant role in computer graphics and visualization. Numerous surface remeshing methods have been developed to produce high quality meshes. Generally, the mesh quality is improved in terms of vertex sampling, regularity, triangle size and triangle shape. Many of such surface remeshing methods are based on Delaunay refinement. In particular, some surface remeshing methods generate high quality meshes by performing the planar Delaunay refinement on the conformal uniformization domain. However, most of these methods can only handle topological disks. Even though some methods can cope with high-genus surfaces, they require partitioning a high-genus surface into multiple simply connected segments, and remesh each segment in the parameterized domain.In this work, we propose a novel surface remeshing method based on uniformization theorem using dynamic discrete Yamabe flow and Delaunay refinement, which is capable of handling surfaces with complicated topologies, without the need of partitioning. The proposed method has the following merits: Dimension deduction, it converts all 3D surface remeshing to 2D planar meshing; Theoretic rigor, the existence of the constant curvature measures and the lower bound of the corner angles of the generated meshes can be proven. Experimental results demonstrate the efficiency and efficacy of our proposed method.

Fabrication of controllable mesh layers above SiNx micro pores with ZnO nanostructures

Ultra-long and laterally aligned Zinc Oxide (ZnO) nanorod arrays were directly synthesized around the edges of SiNx micro pores by using a facile and effective chemical vapour deposition process without any catalysts or additives. ZnO nanorods can grow controllably with a preferential orientation as a bridge beyond the edges and gradually seal into a planar free-standing mesh layer. The optimized growth parameters have been thoroughly investigated and identified. A vapour solid synthesis mechanism with source vapour flow rate control has been tentatively proposed on the basis of the experimental data to explain the synthesis: ZnO nanodots first form around the edges of pores due to the local large binding energy and high Zinc (Zn) vapour concentration, and subsequently nanorods grow epitaxially from the nanodots. This precisely-controlled micro pore sealing approach is an important step toward a coherent mechanism for applications in DNA extraction, separation and the next generation DNA sequencing.

Robust Multiview Photometric Stereo Using Planar Mesh Parameterization.

We propose a robust uncalibrated multiview photometric stereo method for high quality 3D shape reconstruction. In our method, a coarse initial 3D mesh obtained using a multiview stereo method is projected onto a 2D planar domain using a planar mesh parameterization technique. We describe methods for surface normal estimation that work in the parameterized 2D space that jointly incorporates all geometric and photometric cues from multiple viewpoints. Using an estimated surface normal map, a refined 3D mesh is then recovered by computing an optimal displacement map in the same 2D planar domain. Our method avoids the need of merging view-dependent surface normal maps that is often required in conventional methods. We conduct evaluation on various real-world objects containing surfaces with specular reflections, multiple albedos, and complex topologies in both controlled and uncontrolled settings and demonstrate that accurate 3D meshes with fine geometric details can be recovered by our method.

Modelling the tensile failure of composites with the floating node method

This paper presents the modelling of tensile failure of composites using novel enriched elements defined based on the floating node method. An enriched ply element is developed, such that a matrix crack can be modelled explicitly within its domain. An enriched cohesive element is developed to incorporate the boundaries of matrix cracks on the interface, such that the local stress concentrations on the interface can be captured. The edge status variable approach allows the automatic propagation of a large number of matrix cracks in the mesh. A laminate element is formed, such that a fixed, planar mesh can be used for laminates of arbitrary layups. The application examples demonstrate that the proposed method is capable of predicting several challenging scenarios of composites tensile failure, such as the large number matrix cracks, grip-to-grip longitudinal splits, widespread delamination, explosive splitting and distributed fibre breaking in the 0 plies, etc. The complete failure process of ply-blocked composite laminates, up to the final breaking of the loosened 0° strips, is here firstly reproduced by modelling.

Generalized As‐Similar‐As‐Possible Warping with Applications in Digital Photography

AbstractDiscrete conformal mappings of planar triangle meshes, also known as the As‐Similar‐As‐Possible (ASAP) mapping, involve the minimization of a quadratic energy function, thus are very easy to generate and are popular in image warping scenarios. We generalize this classical mapping to the case of quad meshes, taking into account the mapping of the interior of the quad, and analyze in detail the most common case ‐ the unit grid mesh. We show that the generalization, when combined with barycentric coordinate mappings between the source and target polygons, spawns an entire family of new mappings governed by quadratic energy functions, which allow to control quite precisely various effects of the mapping. This approach is quite general and applies also to arbitrary planar polygon meshes.As an application of generalized ASAP mappings of the unit grid mesh, we demonstrate how they can be used to warp digital photographs to achieve a variety of effects. One such effect is modifying the perspective of the camera that took a given photograph (without moving the camera). A related, but more challenging, effect is re‐photography ‐ warping a contemporary photograph in order to reproduce the camera view present in a vintage photograph of the same scene ‐ taken many years before with a different camera from a different viewpoint. We apply the generalized ASAP mapping to these images, discretized to a unit grid. Using a quad mesh (as opposed to a triangle mesh) permits biasing towards affine maps of the unit squares. This allows the introduction of an As‐Affine‐As‐Possible (AAAP) mapping for a good approximation of the homographies present in these warps, achieving quite accurate results. We demonstrate the advantages of the AAAP mapping on a variety of synthetic and real‐world examples.

Facile fabrication of properties-controllable graphene sheet.

Graphene has been received a considerable amount of attention as a transparent conducting electrode (TCE) which may be able to replace indium tin oxide (ITO) to overcome the significant weakness of the poor flexibility of ITO. Given that graphene is the thinnest 2-dimensional (2D) material known, it shows extremely high flexibility, and its lateral periodic honeycomb structure of sp2-bonded carbon atoms enables ~2.3% of incident light absorption per layer. However, there is a trade-off between the electrical resistance and the optical transmittance, and the fixed absorption rate in graphene limits is use when fabricating devices. Therefore, a more efficient method which continuously controls the optical and electrical properties of graphene is needed. Here, we introduce a method which controls the optical transmittance and the electrical resistance of graphene through various thicknesses of the top Cu layers with a Cu/Ni metal catalyst structure used to fabricate a planar mesh pattern of single and multi-layer graphene. We exhibit a continuous transmittance change from 85% (MLG) to 97.6% (SLG) at an incident light wavelength of 550 nm on graphene samples simultaneously grown in a CVD quartz tube. We also investigate the relationships between the sheet resistances.

Optimizing the geometrical accuracy of curvilinear meshes

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Haudorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a particular role of the enhanced mesh boundary smoothness.

Simulation of Electromagnetic Performance on Mesh Reflector Antennas: Three-Dimensional Mesh Structures With Lumped Boundary Conditions

Reflector antennas with mesh surfaces have been extensively used in satellite antenna systems. The electrical contact at the metal–insulator–metal (MIM) junction points may cause the degradation of reflectivity performance, and the concept of MIM junctions is mainly used for the analysis of passive intermodulation (PIM) arising from metallic contact in the practical antennas. In this work, a three-dimensional (3-D) modeling of mesh surfaces is presented, which introduced impedance connections at the wire junctions of metallic contact area. The electrical contact model of impedance connections is equivalent to a circuit model, which is considered as lumped boundary condition extended to the modeling of mesh. The planar mesh reflection coefficients are constructed using a full-wave frequency domain method with Floquet mode expansion. To calculate the electrical performance of curved mesh antenna, a solid surface with an equivalent loss is adopted to replace the mesh surfaces. The reflection coefficients of the equivalent loss material are the same as for the mesh surfaces. The analysis of the planar mesh reflectors with three different connections (solid surface, perfect contact, and lumped connection) at junction points is performed as an example for the proposed model. The results demonstrate the usefulness of the model in accurate performance prediction of mesh reflector antennas. Finally, a mesh reflector antenna with 3-D mesh structures is analyzed to predict the electrical performance of the antenna.

Reply to Comment to: A systematic review of the surgical treatment of large incisional hernia. T. Georgiev-Hristov, A. Celdrán. Hernia 2015; 19:89-101.

We thank Tihomir Georgiev-Hristov and Angel Celdran for their comment on our review on the surgical treatment of large incisional hernias. The authors suggest a double-mesh technique for the closure of large incisional hernias. The results of our review are in line with their statement that the use of a mesh reduces the recurrence rate. The use of two meshes in different planes of the abdominal wall is an interesting concept. However, as they describe in their comment, all articles on ‘double mesh’ techniques advocate a different surgical repair. Meshes are placed in different planes of the abdominal wall, some techniques are bridging, others insist on midline closure, even applying additional releases or component separation techniques. The varying techniques make it different to compare outcomes and complication rates. We would like to encourage a high-quality cohort study with a clearly described double-mesh technique to make the results of this technique comparable to the techniques reported in our review.

Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation

Smoothing is one of the basic procedures for improvement of mesh quality. In this paper, a novel and efficient smoothing approach for planar and surface mesh based on element geometric deformation is developed. The presented approach involves two main stages. The first stage is geometric deformation of all the individual elements through a specially designed two-step stretching-shrinking operation (SSO), which is performed by moving the vertices of each element according to a certain rule in order to get better shape of the element. The second stage is to determine the position of each node of the mesh by a weighted average strategy according to quality changes of its adjacent elements. The suggested SSO-based smoothing algorithm works efficiently for triangular mesh and can be naturally expanded to quadrilateral mesh, arbitrary polygonal mesh, and mixed mesh. Combined with quadratic error metric (QEM), this approach may be also applied to improve the quality of surface mesh. The proposed method is simple to program and inherently very suitable for parallelization, especially on graphic processing unit (GPU). Results of numerical experiments demonstrate the effectiveness and potential of this method.

Innovative Reinforced Soil Structures for High Walls and Slopes Combining Polymeric and Metallic Reinforcements

The aim of the paper is to describe the main advantages of using innovative engineered systems to build reinforced soil structures compared to traditional ones. In particular the paper refers to “hybrid” systems which combine planar polymeric reinforcements (geogrids) and steel wire mesh units in order to build high MSE walls (inclination ≥ 70°, up to almost 90°) or slopes (inclination < 70°). Both the components act as reinforcements and as stabilizing elements. Geogrids are considered to work as primary reinforcements since they guarantee the overall and compound internal stability of the structure. Whereas the wire mesh units are considered a secondary reinforcement providing the local stability at the facing, ensuring that no local mechanism of direct sliding, pull-out or rotational failure occurs. Results on existing structures indicate that, as structures achieve relevant heights (above 10 m), there is a large potential for cost effectiveness in using wire mesh and grids combined, in place of a 100% geogrids or a 100% steel mesh reinforcement solution only [1,2]. Very high hybrid structures have been built all over the world following the mentioned approach. With this paper, three relevant case histories are presented. Firstly, a 80 m high reinforced soil hybrid structure built as retaining structure for a new airport construction in India. Secondly, a 40 m high reinforced soil hybrid structure, built as support for the construction of a highway in Albania. Thirdly, a reinforced soil hybrid structure, up to 16 m high, built as support for heavy tanks of an oil refinery in Turkey, which has been recently fully instrumented.

Mesh improvement by minimizing a weighted sum of squared element volumes

Summary We describe a new mesh smoothing method that consists of minimizing the sum of squared element volumes over the free vertex positions. To the extent permitted by the fixed vertices and mesh topology, the resulting mesh elements have uniformly distributed volumes. In the case of a triangulation, uniform volume implies well-shaped triangles. If a graded mesh is required, the element volumes may be weighted by centroidal values of a sizing function, resulting in a mesh that conforms to the required vertex density. The method has both a local and a global implementation. In addition to smoothing, the method serves as a simple parameter-free means of untangling a mesh with inverted elements. It applies to all types of meshes, but we present test results here only for planar triangle meshes. Our test results show the new method to be fast, superior in uniformity or conformity to a sizing function, and among the best methods in terms of triangle shape quality. We also present a new angle-based method that is simpler and more effective than alternatives. This method is directly aimed at producing well-shaped triangles and is particularly effective when combined with the volume-based method. It also generalizes to anisotropic mesh smoothing. Copyright © 2014 John Wiley & Sons, Ltd.

Designing N‐PolyVector Fields with Complex Polynomials

AbstractWe introduce N‐PolyVector fields, a generalization of N‐RoSy fields for which the vectors are neither necessarily orthogonal nor rotationally symmetric. We formally define a novel representation for N‐PolyVectors as the root sets of complex polynomials and analyze their topological and geometric properties. A smooth N‐PolyVector field can be efficiently generated by solving a sparse linear system without integer variables. We exploit the flexibility of N‐PolyVector fields to design conjugate vector fields, offering an intuitive tool to generate planar quadrilateral meshes.

Summary on several key techniques in 3D geological modeling.

Several key techniques in 3D geological modeling including planar mesh generation, spatial interpolation, and surface intersection are summarized in this paper. Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling. There are two essential procedures in 3D geological modeling: the first is the simulation of geological interfaces using geometric surfaces and the second is the building of geological objects by means of various geometric computations such as the intersection of surfaces. Discrete geometric surfaces that represent geological interfaces can be generated by creating planar meshes first and then spatially interpolating; those surfaces intersect and then form volumes that represent three-dimensional geological objects such as rock bodies. In this paper, the most commonly used algorithms of the key techniques in 3D geological modeling are summarized.

Electric Dipole Antenna in Presence of a Double Wire-Mesh Planar Interference Filter

In this letter, we derive a new full-wave analytical field solution for the problem of two separated planar thin-wire meshes excited by a short horizontal electric dipole (HED). Both meshes are constructed from identical perfectly conducting parallel wires with small period (interwire spacing) compared to wavelength. A fast-converging solution is obtained employing averaged boundary conditions and image theory approach. A set of computed near- and far-field patterns is presented.